Girl engrosses soldiers with martial art (6)
I believe the answer is:
karate
'martial art' is the definition.
(karate is a kind of martial art)
'girl engrosses soldiers' is the wordplay.
'girl' becomes 'kate' (**).
'engrosses' indicates putting letters inside.
'soldiers' becomes 'ra' (abbreviation for Royal Artillery).
'kate' going around 'ra' is 'KARATE'.
'with' is the link.
(Other definitions for karate that I've seen before include "Unarmed-combat system" , "Japanese martial art" , "Japanese form of unarmed combat" , "Martial art (with chopping?)" , "Combative sport" .)