Deal with danger, losing height (5)
I believe the answer is:
treat
'deal with' is the definition.
(synonyms)
'danger losing height' is the wordplay.
'danger' becomes 'threat' (threat can mean a danger or risk).
'losing' indicates named letters should be taken away.
'height' becomes 'h' (abbreviation in geometry).
'threat' with 'h' taken out is 'TREAT'.
(Other definitions for treat that I've seen before include "Pay for someone else's enjoyment" , "Behave towards" , "Engage in negotiations" , "Pay for someone's food or drink or look after them medically" , "Tetra (anag.)" .)