Head girls love to run the gauntlet (5)
I believe the answer is:
glove
'gauntlet' is the definition.
(I've seen this in another clue)
'head girls love' is the wordplay.
'head' says to take the initial letters.
The initial letter of 'girls' is 'g'.
'g'+'love'='GLOVE'
'to run the' is the link.
This may not be correct. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for glove that I've seen before include "protective wear on" , "Hand cover" , "Proverbially good fitter" , "hands warmer" , "Mitten" .)