Wearing glasses, run in to manage light-splitting instrument (12)
I believe the answer is:
spectroscope
'instrument' is the definition.
(spectroscope is a kind of instrument)
'wearing glasses run in to manage' is the wordplay.
'wearing' indicates putting letters inside.
'glasses' becomes 'specs' (short for spectacles).
'run in to' becomes 'tro' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'manage' becomes 'cope' (manage can mean to cope or do well).
'specs' enclosing 'tro' is 'spectros'.
'spectros'+'cope'='SPECTROSCOPE'
'light-splitting' is the link.
This may not be right. It may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for spectroscope that I've seen before include "Device splitting different wavelengths of radiation" , "Scientific device for splitting light" , "Instrument for observing light of different wavelengths" .)