Entrance to missing seismometer is damaged (9)
I believe the answer is:
mesmerise
'entrance' is the definition.
(I know that entrance is a more specific form of the action mesmerise)
'to missing seismometer is damaged' is the wordplay.
'missing' indicates named letters should be taken away.
'is damaged' is an anagram indicator.
'seismometer' with 'to' taken away is 'seismmeer'.
'seismmeer' anagrammed gives 'MESMERISE'.
(Other definitions for mesmerise that I've seen before include "Hypnotise, spellbind" , "Transfix" , "Fascinate" .)