No. Re-application for H4-EAD and H4 is not required.
H4 and H4-EAD are valid till their expiry. If you change your work location, only the primary H1B beneficiary’s H1B amendment is required.
Normally, employer’s file both H1B and H4 amendment’s to keep the expiry dates in sync.
Otherwise, it is better to save cost on re-applying H4, if the remaining validity is still high.
H4 and H4-EAD remain valid till their validity.
You can go for your primary H1B’s amendment and extension cycles any number of times during this period.
There is no need to renew renew them unless they are about to expire in near future.
You will have to renew the H4 and H4-EAD as and when they are expiring providing your most recent H1B approved petition.
NOTE: If you file for H1B amendment or extension and it is rejected/not approved, and you have to leave country, then, the dependent H4 and H4-EAD which still have validity, does not count.
If you leave the country due to rejected H1B at anytime, your dependent H4 and H4-EAD also have to leave with you.