Even if the number in question is not the prime key of the table, I would not renumber it as long as any other projects above it are still active. The implication is that if you have, say, 50 projects and number 1 goes dormant, you would have to renumber 49 other projects.
If this number is so ephemeral that it gets renumbered every time any other project changes status, and it isn't an autonumber to begin with, don't store it. Doing so would violate at least one normalization rule. (The rule that says a field in a table must depend only on the entire prime key.) This number does not depend on the prime key of only the current record. It depends on the prime keys of other records, too. It does not belong with other data regarding your project.
Compute it in a query by finding an expression such as
1 + DCount( "[ProjPK]", "ProjTable", "[ProjPK] < " & CStr$( [ProjPK] ) )
In other words, order the projects by prime key and this number you want is 1 + the number of projects with lesser prime keys. For the first project (lowest PK), the number is 1.