There isn't really a word for "quest" in Latin
quest (subs.) :
I. A diligent, eager, search (used, in the phr. in quest of: but often absol.) :
1. expr. by subs. (i.) quaesitio, f. : Psyche bent on the q. for Cupid. Psyche quaesitioni Cupidinis intenta, Apul. M. 5, p. 171:
(ii.) inquisitio,f.. ; absol., the q. for truth : .join inquisitio atque investigatio ; Cic. Off.
hominis est propria veri inquisitio atque investigatio, Cic. Off. I, 4, 13: in q. of:
inquisitione (the hyena is said) to be the only beast that rifles tombs in quest of dead bodies, a
b uno animali sepulcra erui inquisitione corporum. Plin. 8, 30.44:
to send a person anywhere in q. of.
mittere ad inqisitionem (with gen. of thing and in of place): cf.
Amyntam cum deceem triremibus in Macedoniam;
ad inq. novorum militum (in q. of recruits).
Curt. 4. 6, Jin. : dat. in the phr. take care I don't come in q. of you, sed tu cave inquisitioni mihi sis, Pl.
Casin. 3. I, fin. (iii.) quaestio, /. (In sim. phr.) :
tibi ne quaestioni essemus, id. Capt. 2. J, J : and in abl. with in,
cave fuas mihi in quaestione. Id. Pers. I, I, 52. (Note: the abl. quaesitu, Plin. 5,9, 10, stadium, a person in q. of, quaesitor, m., Pascal. Pan. Theod. 28 : inquisitor : one in q. of the facts of science,
rerum naturae inquisitor, Sen. Q. N. 6, 13; : cf.
rerum inquisitorem decet esse sapientem, Cic. fr. Acad. ap. Aug. contr. Acad. 2, II: v. inquirer, investigator. [...]