There are two different confrontations with Satan in the future that the passage may relate to: the temptation of Jesus during His Passion and/or the temptation of those who persecuted and betrayed Him.
The Greek phrase is ἄχρι καιροῦ (archi kairou). The word καιρός (kairos) here might be better translated here as opportunity.1 The usually hyper-literal Orthodox New Testament translates the phrase until an opportune time.
Greek commentators on this verse in antiquity seemed to understand the second occasion to have been the time of the Cross. One commentator writes:
And not without meaning are the words, he departed from Him for a time. The devil attacks the Lord by means of two passions, pleasure and grief. He attachd the lord with pleasure when he led Him up onto the mountain. Then the devil departed from Him for a time, that is, until the time of the Cross, when the devil attacked Him again, this time with grief.2
Along these lines, the Russian Orthodox Archbishop Averky Taushev (1906-1976) made a connection with Christ's Agony in the Garden, described in John 17:
At the same time, this agony occurred without a doubt also because the
Lord took upon Himself all the sins of the world, and took them to the
cross. That which the whole world should have been feeling on account
of its sinfulness now was concentrated on Him alone! It is also not
out of the realm of possibility that the devil, who had left Him after
the temptations “until an opportune time” (Luke 4:13), now returned
with new temptations, trying to dissuade Him from His coming Passion,
although without success. The sorrow of Christ the Saviour was also a
result of the knowledge of human cruelty, humanity’s lack of gratitude
to God.3
Augustine suggested that the devil returned in those who later persecuted Jesus:
Satan will return. He will enter Judas and will make him betray his master. He will bring along the Jews, not flattering now, but raging. Taking possession of his own instruments, he will cry out with the tongues of all of them, “Crucify him, crucify him!” (Sermon CCLXXXIV)
Ephraim the Syrian offers a similar interpretation in his commentary on the Diatessaron (a 2nd century Syriac harmony of the Gospels). Another modern Eastern Orthodox commentator, Lawrence Farley, writes:
For Satan departed only until an appointed time and an opportune
moment (Gr. kairos). For Luke such a time came with the betrayal
of Judas, when Christ was betrayed into the hands of His foes. Then
Satan would tear and sift the disciples like wheat (22:31); that would
be the hour for Satan to exercise his dark authority (22:53). But for
now, he had been decisively vanquished.4
1. See, e.g., Swanson's Dictionary of Biblical Languages with Semantic Domains: Greek
2. Theophylact of Ohrid, Explanation of the Holy Gospel According to St. Luke (tr. from Greek; Chrysostom Press, 1997), p.49
3. The Four Gospels: Commentary on the Holy Scripture of the New Testament (tr. from Russian; Holy Trinity Seminary Press, 2015), p.214
4. The Gospel of Luke: Good News for the Poor (Ancient Faith Publishing, 2010), p.100-101