Reciprocally put up (not very quietly) with all my surrounding (8)
I believe the answer is:
mutually
'reciprocally' is the definition.
(synonyms)
'put up not very quietly with all my surrounding' is the wordplay.
'not' is a deletion indicator.
'very quietly' becomes 'pp' (musical abbreviation for pianissimo).
'with' says to put letters next to each other.
'surrounding' is an insertion indicator.
'put'+'up'='putup'
'putup' with 'pp' taken away is 'utu'.
'utu'+'all'='utuall'
'utuall' put within 'my' is 'MUTUALLY'.
(Another definition for mutually that I've seen is " Reciprocally".)