Overheard to whimper like a baby, being cross? (4)
I believe the answer is:
mule
'being cross?' is the definition.
(I've seen this before)
'overheard to whimper like a baby' is the wordplay.
'overheard' indicates a 'sounds like' (homophone) clue.
'to whimper like a baby' becomes 'mewl' (to mewl is to cry feebly).
'mewl' sounds like 'MULE'.
(Other definitions for mule that I've seen before include "Hybrid animal - slipper" , "Obstinate creature" , "Sterile offspring of donkey and horse" , "footwear" , "Obstinate quadruped" .)