"First rent" is a principle of law that applies to certain legal rents and registrations after construction work qualifies renovated apartments as new units. For example, if the landlord changes walls in an apartment with the effect of increasing or decreasing it's overall size, the "first rent" provision may come into play.
When a landlord alters a rent-stabilized unit to transform it into an apartment that did not exist before the construction, he or she may lease it out as a new, unregulated apartment. This may justify a rent increase above one calculated on the base rent charged for the old apartment, even if the difference in rent is beyond amounts the rent stabilization guidelines have established. After all, the landlord's lawyer might argue, the apartment is not the same unit it previously was, in terms of space or configuration, so the first rent doctrine should apply. The fact it was formerly rent-regulated may never be discovered unless a tenant is able to research the building's registration history of rent rolls, alteration permits at the Department of Buildings ("DOB"), amendments to the certificate of occupancy ("C of O") at Housing Preservation and Development ("HPD"), etc.
If the tenant is able to show that the unit is substantially the same as it was before, with only minor alterations, a judge might agree that the apartment should still be rent-stabilized, giving the tenant a right to renew the lease, possibly at a lower rent. You might also be awarded substantial damages for the landlord's overcharging.
If you learn that the landlord claims your unit was reconstructed, do your homework. Check the websites of the DOB for alteration permits and HPD for amendments to C of O filings, and try to get certified rent history printouts for your apartment from Homes and Community Renewal (formerly DHCR, the Department of Housing and Community Renewal).
A Tenant's lawyer might be able to give you further advice in these investigations. Sometimes there are complicated elements to these cases. For example, your unit may have a rent history listed under different apartment numbers. However, it can be worth investing the time to look into details, because in the end you might have a rent overcharge case and get triple damages. There's no guarantee the court will agree with the landlord, and with skillful representation you may win.
Attention New York City Tenants: Get more more information on Landlord Tenant matters at the McAdams Law main site here.