"Shrove" is the past tense of "shrive", meaning "to hear a
confession".
It is most common in the term "Shrove Tuesday" referring to the
fact that Catholics would seek absolution of sins prior to the
beginning of Lent.
"Shrive" comes from the Old English "scrifan", which was used to
mean "prescribing or recommending a confession". This is ultimately
from the Latin "scribo", meaning "to write" (as in "prescribe",
"scribe", "scribble", "script").
The noun form is "shrift". If you're convicted of a capital
offense, you get a "short shrift" prior to your execution. If your
buddies have taken the loot, and you "get the short shrift", then
you've been badly cheated.