Exegesis:

suntelesas panta peirasmon ‘having brought to an end every (i.e. every kind of) temptation.’ For sunteleō cf. on v. 2; it is best rendered in a neutral sense without implications of completing a prearranged plan.

peirasmos ‘temptation,’ here in the active sense, ‘tempting.’

achri kairou lit. ‘until a moment of time’ is interpreted variously: (1) ‘until a certain time,’ i.e. “for a while”, “for a time” (Williams); (2) “until an opportune time” (Revised Standard Version, La Sainte Bible: Nouvelle version Segond révisée), i.e. “till a fit opportunity arrived” (Moffatt); (3) ‘until a fixed time,’ i.e. “until the appointed time” (Translator’s New Testament, Nieuwe Vertaling, Willibrord, Bible de Jérusalem). The first interpretation seems preferable (cf. Acts 13.11).

Translation:

When the devil had ended every temptation. In some cases it is necessary to add a reference to the actor or/and the goal of the tempting, e.g. ‘all the temptations against him’ (Bahasa Indonesia), ‘all the temptations with which he tempted him’ (Sranan Tongo), ‘the devil’s tricks to seduce Jesus’ (Tae’ 1933). A shift to a verbal construction leads to a rendering such as, ‘after the devil had tempted him/Jesus in every way’; and the conative aspect may better be made explicit as in, “when the devil had tried every kind of temptation” (An American Translation), ‘then the devil gave up all his attempts at seducing Him’ (Willibrord).

Until an opportune time, or, following the interpretation preferred in Exegesis, “till another time” (An American Translation, similarly Kituba), ‘for the time being’ (Leyden, Tae’ 1933), or, in a more expanded wording, ‘he (i.e. the devil) said to himself, “There will be another day yet for that” ’ (Tboli).

Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.