Exegesis:

paratērēsantes lit. ‘after watching’ either with auton ‘him,’ i.e. Jesus., understood, or without object in an absolute sense, i.e. ‘watching their opportunity,’ preferably the latter.

egkathetous hupokrinomenous heautous dikaious einai ‘spies who pretended to be righteous.’ dikaious is best interpreted, ‘scrupulous,’ ‘conscientious,’ since it is a matter of doing the right thing.

egkathetos lit. ‘suborned, or hired,’ i.e. to perform a secret commission, hence ‘secret agent.’ Here the commission is to try to catch Jesus in his words.

hupokrinomai ‘to pretend.’ The participial clause hupokrinomenous … einai refers to the method which the agents were to use.

hina epilabōntai autou logou ‘in order that they (i.e. the agents) might catch him in/on a word.’ epilabōntai is best understood as construed with two genitives i.e. the genitive of the person (autou), and the genitive of the thing in which (logou).

hōste paradounai auton tē archē kai tē exousia tou hēgemonos ‘so as to hand him over to the jurisdiction and the authority of the governor.’ hōste with infinitive refers here to the intended result. archē and exousia are probably best understood as a hendiadys.

hēgemōn (also 21.12) ‘governor,’ in itself a general term and applicable to the Roman emperor and his underlings (cf. hēgemoneuō in 2.2, and hēgemonia in 3.1).

Translation:

They watched him, preferably, ‘they looked out for an opportunity,’ “they watched for the right time” (Good News Translation).

An existing receptor language term for spies often does not fit the situation: a term for ‘secret agent’ may not exist in the language. Then one may have to use a descriptive phrase, e.g. ‘men secretly commissioned/told/persuaded,’ ‘people hired/bribed’; such a phrase may have to be connected with the following ‘that’-clause, which indicates what they were commissioned (etc.) to do.

Pretended to be sincere, or, ‘posed as conscientious people,’ ‘played the conscientious’ (Bible de Jérusalem), ‘acted as conscientious though they were not.’ Sincere, preferably, ‘conscientious,’ ‘strict/punctilious (in their behaviour),’ especially in their observance of the religious law.

That they might take hold of what he said, or, ‘to ensnare him in an utterance-of-his’ (Bahasa Indonesia RC), ‘to catch-him-like-a-fish with-reference-to his words’ (Trukese, Pohnpeian), ‘to spy on him till he would miss his mouth (i.e. make a mistake in speaking)’ (Sranan Tongo), ‘that they would be able to find his sin if his words became bad’ (Tzeltal).

So as to, or, ‘so that they could,’ ‘which would enable them’; usually better as a new sentence, e.g. ‘Thus they expected to be able to…,’ ‘Thus they might…’ (Leyden).

Deliver him up, or, ‘turn/hand him over,’ ‘seize and bring him.’ The verb in itself neutral, has in this context a pejorative meaning, but less so than ‘to betray’ (cf. on 6.16), since it does not presuppose a violation of allegiance.

The authority and jurisdiction of the governor, or, ‘the power and authority of the governor,’ ‘the hand(s) (in the sense of ‘power’) and authority of the governor,’ ‘the supreme-power of the governor’ (Willibrord). If the verb only takes a personal indirect object, one may shift to, ‘the governor, who had authority and jurisdiction (over him),’ cf. ‘the governor, he being the one who had power and authority’ (Shona 1966), ‘the one in authority’ (Zarma), ‘those who (were) in power (to) watch over the land’ (Ekari) For governor see on 2.2.

The rather intricate sentence pattern may have to be recast, especially where “spies” has to be rendered by a descriptive phrase, and/or the linguistic and historical order should closely parallel each other. This may result e.g. in, ‘They watched their chance and intended (or hoped to be able) to deliver him to … the governor. Therefore they secretly commissioned some men, who were to pose as conscientious people, and sent them to catch him in his words (or, commissioned some men and sent them to catch him in his words. To do so these men were to pose as conscientious people).’

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.