Close your eyes, lacking the heart for experiences (7)
I believe the answer is:
endures
'for experiences' is the definition.
(enduring is a kind of experiencing)
'close your' is the wordplay.
'close' becomes 'end' (close can mean to end or finish).
'your' becomes 'ures' (I can't explain this - if you can you should give a lot more credence to this answer).
'end'+'ures'='ENDURES'
'eyes lacking the heart' acts as a link.
This may not be right. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for endures that I've seen before include "Remains firm" , "Lasts or puts up with" , "Suffers or lasts" , "Bears" , "Ensured (anag.)" .)