I strained muscle at first, going out for run (10)
I believe the answer is:
administer
'run' is the definition.
(thesaurus)
'i strained muscle at first going out' is the wordplay.
'at first' suggests taking the first letters.
'going out' indicates an anagram (out can mean wrong or inaccurate).
The initial letter of 'muscle' is 'm'.
'i'+'strained'+'m'='istrainedm'
'istrainedm' anagrammed gives 'ADMINISTER'.
'for' acts as a link.
(Other definitions for administer that I've seen before include "act as manager" , "Deal out (punishment)" , "Oversee" , "give" , "control" .)