Soothe Republican First Lady hosting priest from Israel (7)
I believe the answer is:
relieve
'soothe' is the definition.
(relieve can mean to soothe)
'republican first lady hosting priest from israel' is the wordplay.
'republican' becomes 'r' (abbreviation).
'first lady' becomes 'eve' (first woman in the Bible).
'hosting' indicates putting letters inside (inserted letters are welcomed in or hosted).
'priest from israel' becomes 'Eli' (high priest of the Israelites in the Bible).
'r'+'eve'='reve'
'reve' enclosing 'eli' is 'RELIEVE'.
(Other definitions for relieve that I've seen before include "Take a job over from - bring aid" , "Alleviate (eg, pain)" , "Break the sameness of" , "Take over (from) - ease worries (of)" , "Make less tedious, bring aid to (besieged place)" .)