A tendency or inclination to steal things.
I think the new cashier we hired has sticky fingers, because money has begun disappearing from the till on the days that he's working.
Someone with sticky fingers has been taking supplies out of the office.
ENGLISH IDIOMS TO NATIVE SPEAKERS:
**** COMMONPLACE: very frequently used, everyone knows it and most people use it, and a must-know for EFL learners, 1000/3000
*** COMMON: frequently used, almost everyone knows it and a considerable portion of people use it, the more an EFL learner knows the better it is, -3000/-5000
** UNUSUAL: unknow to a considerable portion of the native speakers, but they can usually understand when hearing them, the EFL learners can just resort to dictionaries when encountering them
* RARE: even unknown to most native speakers, and a considerable of them can not manage to understand without coming to dictionaries