Veteran soldier in TA slowed alarmingly (3,5)
I believe the answer is:
old sweat
'veteran soldier' is the definition.
(I've seen this before)
'ta slowed alarmingly' is the wordplay.
'alarmingly' is an anagram indicator (I've seen this in other clues).
'ta'+'slowed'='taslowed'
'taslowed' with letters rearranged gives 'OLD SWEAT'.
'in' acts as a link.
(Other definitions for old sweat that I've seen before include "Very experienced chap" , "Veteran, one expected to 7" , "Veteran soldier" .)