Be inclined to rely rashly on going carefully! (8)
I believe the answer is:
tenderly
'carefully' is the definition.
(thesaurus)
'be inclined to rely rashly on' is the wordplay.
'be inclined' becomes 'tend' (synonyms).
'rashly' is an anagram indicator.
'on' is an insertion indicator (as in clothing \'on\' a person).
'rely' anagrammed gives 'erly'.
'tend' placed into 'erly' is 'TENDERLY'.
'going' is the link.
This may not be right. It may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for tenderly that I've seen before include "with compassion" , "Sensitively" , "In gentle and loving manner" , "In gentle and fond manner" , "Gently, sympathetically" .)