run a risk vs seek

run a risk is not a noun while seek is a noun.

Word	Noun	Adjective	Verb	Adverb
run a risk	No	No	Yes	No
seek	Yes	No	Yes	No

As verbs, seek is a hypernym of run a risk; that is, seek is a word with a broader meaning than run a risk:

Other hypernyms of run a risk include assay, attempt, essay, try.

run a risk (noun)	seek (noun)
	the movement of a read/write head to a specific data track on a disk

run a risk (verb)	seek (verb)
take a risk in the hope of a favorable outcome	inquire for
	try to locate or discover, or try to establish the existence of
	go to or towards
	try to get or reach
	make an effort or attempt