If you don't receive Social Security yet, you can apply for a reduced benefit when you turn 62 or wait until your full retirement age if you want to receive an unreduced spousal retirement benefit. If you've been divorced for more than two years, you can apply as soon as your former spouse becomes eligible for benefits, even he or she hasn't started receiving them (assuming you're at least 62). However, if you've been divorced for less than two years, you must wait to apply for benefits based on your former spouse's earnings record until he or she starts receiving benefits.
You don't have to worry about losing your benefit even if your former spouse remarries. Benefits for a divorced spouse are calculated separately from those of a current spouse.