For the most part, Klingon doesn't often use nouns to speak of moods, states or behaviors; it is more likely to use verbs.
For example, rather than saying "She is renowned for her cunning.", you would be more likely to see a sentence like 'ongmo' noy. ("Because she/he is cunning, she/he is well-known."), using the verbs 'ong ("be cunning, be sly") and noy ("be famous, be well-known").
There are certainly exceptions to this, with words for things like courage (toDuj), pride (le'yo') and QeH ("anger"), but they are relatively rare.
It is also possible to nominalize verbs, but it's not really all that common, and often leads to unnatural-sounding sentences.
So, is there a known word for "be curious"? As it turns out, there is not. We are left trying to explain the state of being curious through the use of existing terminology.
ghojqang - she/he/they is/are willing to learn - formed from ghoj ("learn") and the volitional suffix -qang ("willing")
ghojqangqu' - she/he/they is/are really willing to learn - like ghojqang, but with the willingness
poymar paQ 'e' tIv - she/he enjoys contemplating mysteries
yaj 'e' nIDqu' - she/he really tries to understand
pIj vuQlu' - she/he is frequently fascinated
reH yabDaj je' neH - she/he always wants to feed her/his mind - There is a Klingon saying: yab wIje'meH maSuv. ("We fight to enrich the spirit."). Perhaps a studious person would rather say qa' wIje'meH maHaD. ("We study to enrich the mind.")
ghung yabDaj - her/his mind is hungry - I don't know if this would be common expression among Klingons, but I suspect it would get the message across.
If you really need a noun, you could try nominalizing one of them (i.e. ghojqangghach - "a willingness to learn") or using a relative clause (i.e. DI'on'e' chIwbogh yab ghung - "the characteristic embodied by a hungry mind").