I'm obliged to admit blunder, tailing old men (5,5)
I believe the answer is:
other ranks
'men' is the definition.
(other ranks are a type of soldiers)
'i'm obliged to admit blunder tailing old' is the wordplay.
'i'm obliged' becomes 'thanks' (if you thank someone you are obliged to them).
'to admit' indicates putting letters inside.
'blunder' becomes 'err' (I've seen this before).
'tailing' means one lot of letters go next to another (to tail can mean to go after or follow).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'thanks' enclosing 'err' is 'therranks'.
'therranks' after 'o' is 'OTHER RANKS'.
(Other definitions for other ranks that I've seen before include "Non-commissioned types" , "Most of the men who fight" , "Armed forces members not holding commissions" , "Enlisted troops" , "Non-commissioned armed forces members" .)