Learner with tatty grey hat showing lack of energy (8)
I believe the answer is:
lethargy
'lack of energy' is the definition.
(I've seen this before)
'learner with tatty grey hat' is the wordplay.
'learner' becomes 'l' (as in a learner driver with L-plates on their car).
'with' is a charade indicator (letters next to each other).
'tatty' is an anagram indicator (I've seen this in other clues).
'grey'+'hat'='greyhat'
'greyhat' with letters rearranged gives 'ethargy'.
'l'+'ethargy'='LETHARGY'
'showing' is the link.
(Other definitions for lethargy that I've seen before include "'Lassitude, langour (8)'" , "Stringed instrument" , "Sloth" , "Lack of vitality or energy" , "Unnatural drowsiness" .)