Collocations for prestige - noun

considerable, enormous, great, high, immense
Winning the prize carries immense prestige.

low
international, national
occupational (AmE), personal
academic, intellectual, political, social

enjoy, have
an international company that enjoys immense prestige

lack
acquire, derive (from sth), gain, get
Lavish hospitality allows the host to gain prestige.

accord sb/sth, attach to sb/sth, give sb/sth
Different jobs are accorded different levels of prestige.

bring, carry, confer, lend
Owning landed property confers prestige.

lose
boost, enhance, increase, raise
damage, lower
The couple's prestige was damaged by the allegations.

prestige among, prestige with
the party's prestige among the public

prestige within
The post carried great prestige within the police force.

a loss of prestige
Doctors have suffered a loss of prestige following a spate of scandals.