Bear with sore head and dog, Mud, get on in no time (10)
I believe the answer is:
curmudgeon
'bear with sore head' is the definition.
'curmudgeon' can be an answer for 'bear' (both can mean a bad-tempered person). I am unsure of the 'with sore head' bit.
'dog mud get on in no time' is the wordplay.
'dog' becomes 'cur' (a cur is an aggressive or scruffy dog).
'get on' means one lot of letters go next to another (in a down clue, some letters go above others).
'in no time' becomes 'geon' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'cur'+'mud'+'geon'='CURMUDGEON'
'and' is the link.
Can you help me to learn more?
(Other definitions for curmudgeon that I've seen before include "Malcontent, grouch" , "Cranky oldster" , "Bear" , "Churlish miser" , "Meldrew, say" .)