"rely on fear" is a correct and usable phrase in written English.
You can use this phrase when you want to express that someone or something is using fear to gain or sustain control or influence. For example: The dictator relied on fear to keep the citizens in line.
Police departments usually rely on fear and lobbying to beat reforms back; police reformers can't let them this time.
Pushka Gautam, a Katmandu-based writer who was a Maoist commander until he defected in 2000, says they now rely on fear.
Acts that are "faith-based" stand a good chance of being beneficial to humanity, but not a better chance than acts that are skepticism-based--that is, grounded in an understanding of morality that does not rely on fear (or love) of divine authority (or any other kind of authority, for that matter).
A similar premise applies to phishing emails, which rely on fear and intimidation to prompt recipients to click on links that lead to bogus bank web sites or deliver viruses and Trojans to the user's computer.
We used to be able to rely on fears of HIV and the Aids epidemic's devastation to encourage (or even coerce) people to use condoms and get tested – but that doesn't work as well as it used to.
Later it relied on fear and terror wielded by a ferociously effective secret police.
Ms. Rhee and Beverly Hall, the former Atlanta superintendent, both relied on fear to motivate, relentlessly driving their work forces.
We need to abandon the current government approach that relies on fear of harms underpinned by ignorance of what drugs users are taking as the prime approach.
The more rigid, fact-driven Russian system, by contrast, relies on "fear and pressure", meted out by older, Soviet-trained teachers.
He divided the country along "fault lines of fear", according to Maureen Dowd in the New York Times; he relied on "fear of and hatred for modernity", added Garry Wills, polymath and devout Catholic.
