The crux of this verse is to understand the meaning of "suffering". It is crucial that we understand "suffering" means not the modern and more popular sense of "undergoing pain" or at any rate not just that. It mainly serves as a counterpart concept in Eliot's poetry to "action". If we read it as pain we wouldn't be able to see its close connection with patience and action.
Note that in his work Eliot is invoking a somewhat archaic sense of the word "suffer", after all this is a play Eliot composed about a historical event that took place in the 12th century. According to Merriam Webster:
to allow especially by reason of indifference
the eagle suffers little birds to sing
— William Shakespeare
You suffer something or someone means you allow them to perform an action by reason of indifference. That is, you don't care the action is taken or not. It makes no difference to you. No skin off your back. You are a passive party in the performance of the action; you are a patient. Here the word patient is also to be understood differently from the prevalent modern usage (an individual under medical treatment). Again, see Merriam Webster's definition of patient:
one that is acted upon
are agents as well as patients and observers in the world
— C. H. Whiteley
This is not to say suffering does not have the meaning of enduring or undergoing misery or pain. It does. But that sense of the word is kind of secondary to the "pain" interpretation, at least not primordial. That is why Louis L. Martz in his literary criticism essay The Wheel and the Point: Aspects of Imagery and Theme in Eliot's Later Poetry1 wrote:
One must first recognize the double meanings in the words, suffering, patient, and patience. Suffering is not simply undergoing misery or pain, it is also permitting, consenting; he who consents to an action must suffer for it, must accept responsibility for it. The Chorus of Women of Canterbury, the "type of the common man," understands no such responsibility as the play begins: "For us, the poor, there is no action,/But only to wait and to witness." It is this responsibility that the women strive to evade as they realize they are being "drawn into the pattern of fate"; this is what they finally admit at their great moment of exaltation and vision: "I have consented, Lord Archbishop, have consented." It is the admission of sin which Eliot describes and demands in his prose writings--in the essay on Baudelaire's Journaux Intimesy for example, where he insists that "the recognition of the reality of Sin is a New Life," and finds the greatness of Baudelaire (like the greatness of the Chorus here) to reside in his capacity for suffering pain in the knowledge of good which comes from the recognition of evil. It is the view expressed in one of Eliot's notes to The Idea of a Christian Society. "The notion of communal responsibility, of the responsibility of every individual for the sins of the society to which he belongs, is one that needs to be more firmly apprehended."
Thus, too, the patient is everyone, martyr, murderer, and spectator: he is at once suffering pain and permitting action; in Becket and the Chorus, he is also self-controlled. The same ideas are seen in the lyric of "East Coker," where the "hospital" patient is saved by Christ from "Adam's curse": "Beneath the bleeding hands we feel/The sharp compassion of the healer's art.
Martz makes the argument that Eliot's poetry puts action in the same position as suffering. Suffering is action and of action, which means suffering comes from action but also identifies with action. At the same time action has the same identification effect and causality on suffering.
As I said above, we can discern two distinguishable meanings of "suffer". To experience anguish or torment and to have something done to you. Suffering thus signifies passive acceptance or passive endurance, submission. Action, on the other hand, is actively doing things (to others). From this Eliot develops a conceptual double correspondence:
Here some scholars see suffering taking on a third (or second) connotation. Paul Lapworth argues:
Thomas's words at this point span the developing experience of the Chorus. What happens to us is one thing; understanding and knowledge of what happens to us is another. We are aware of experiencing something, but we cannot explain its significance. This is a double suffering. The Chorus know (are aware) that they are suffering; they do not know (do not understand) the significance of what is happening to them. When they understand and consent, then action and suffering are one.2
I'd like to add that I see it as a third connotation, not a second meaning, because we have to take into account the first two meanings that I mentioned above. Granted this new connotation should be subsumed under the suffering sense, so not a full-fledged independent meaning. The Chorus are both in the know and in the dark. They are only partially aware of what is happening and the action taken on them. They do not take an active part in what they see as bound to happen. Action is an individual's strong will to change their own fate. Suffering is passive acceptance of one's fate as inevitable.
Immediately after your quoted verse the poem goes:
That the pattern may subsist, for the pattern is the action
And the suffering, that the wheel may turn and still
Be forever still.
Conjuring up "the wheel" Eliot explains the action/suffering duality through the order of the universe, created by God and willed to move by God. To understand Eliot's further ideas about the will of God we would have to go beyond this quoted verse. To sum, through Thomas Becket Eliot argues one must willfully submit to God's will, thus bring suffering and action together. Suffering thus is action, and duality becomes one.
1The Sewanee Review Vol. 55, No. 1 (Jan. - Mar., 1947), pp. 126-147
2Murder in the Cathedral by T. S. Eliot, Paul Lapworth, Macmillan International Higher Education, Nov 11, 1988, p 15