Student regularly nicked carrying a weapon (5)
I believe the answer is:
lance
'weapon' is the definition.
(lance is a kind of weapon)
'student regularly nicked carrying a' is the wordplay.
'student' becomes 'l' (as in L-plates for learner drivers).
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'carrying' says to put letters next to each other (in a down clue, the bottom letters carry others).
The alternating letters of 'nicked' are 'nce'.
'nce' put after 'a' is 'ance'.
'l'+'ance'='LANCE'
(Other definitions for lance that I've seen before include "Weapon of knights of old" , "A horse soldier's spear" , "Horseman's long spear" , "surgical instrument" , "Spear for a horse-soldier" .)