One bringing up issue that's arisen with mud wrestling (9)
I believe the answer is:
nursemaid
'one bringing up issue' is the definition.
The answer is a person as well as being a singular noun. This is suggested by the definition.
'arisen with mud wrestling' is the wordplay.
'with' means one lot of letters go next to another.
'wrestling' indicates anagramming the letters.
'arisen' put after 'mud' is 'mudarisen'.
'mudarisen' with letters rearranged gives 'NURSEMAID'.
'that's' is the link.
Can you help me to learn more?
(Other definitions for nursemaid that I've seen before include "employ one for small charge" , "Woman employed to look after children" , "child minder" , "tender" , "Childminder" .)