Adult with cold, terrible snot: need strong tissue? (8,6)
I believe the answer is:
achilles tendon
'strong tissue?' is the definition.
(tissue in the body)
'adult with cold terrible snot need' is the wordplay.
'adult' becomes 'a' (abbreviation).
'with' means one lot of letters go next to another.
'cold' becomes 'chill' (chill can mean cold).
'terrible' indicates an anagram.
'snot'+'need'='snotneed'
'snotneed' anagrammed gives 'estendon'.
'a'+'chill'+'estendon'='ACHILLES' TENDON'
(Other definitions for achilles tendon that I've seen before include "sinew" , "part of leg" , "part of body" , "accident spot" , "Tissue" .)