You do not need to apply separately for the Federal Pell Grant and there is no deadline to be eligible for the Pell Grant.
Federal Pell Grant
Federal Pell Grants are awarded to students based on information provided on the FAFSA. The amount of your Federal Pell Grant depends on your cost of attendance, expected family contribution and enrollment status. Eligibility for other federal and non-federal grants may be based on eligibility for the Federal Pell Grant. With a few exceptions, Federal Pell Grants are available only to undergraduate students for a maximum lifetime limit of 12 semesters or its equivalent.