Exegesis:

exōmologēsen ‘he consented,’ ‘he agreed.’ exomologeō in 10.21 in a different meaning.

ezētei eukairian ‘he sought an opportunity,’ ‘he looked for a chance.’ The imperfect tense of ezētei is durative.

eukairia ‘favourable opportunity.’

tou paradounai auton … autois ‘to hand him over to them,’ articular infinitive in the genitive, dependent upon eukairian.

ater ochlou lit. ‘without a crowd,’ i.e. ‘without a crowd being present,’ or ‘without tumult,’ preferably the former.

ater (also v. 35) ‘apart from,’ ‘without.’

Translation:

He agreed, preferably, ‘he consented,’ ‘he accepted their proposal’ (Willibrord), ‘he said it was all right.’

In the absence of the multitude, or, ‘without the crowd knowing about it’ (cf. Good News Translation), ‘when the crowd would not be present, or, aware of it.’

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.