Extreme mutt's barking outside back of Tesco (6)
I believe the answer is:
utmost
'extreme' is the definition.
(synonyms)
'mutt's barking outside back of tesco' is the wordplay.
'barking' is an anagram indicator (UK slang for mad).
'outside' is an insertion indicator (some letters go outside others).
'back of' suggests the final letters.
The final letter of 'tesco' is 'o'.
'mutts' is an anagram of 'utmst'.
'utmst' enclosing 'o' is 'UTMOST'.
(Other definitions for utmost that I've seen before include "(To the) maximum extent" , "(To the) greatest possible extent" , "Ultimate" , "Furthest or extreme" , "'Most extreme, greatest (6)'" .)