Yes, there will be a short gap and you can’t continue working during the gap.
OPT as soon as SEVIS is transferred out of the original school. You can restart working after obtaining the new CPT I-20 from the new school. To start working on the first day, we recommend that you start your CPT application as soon as possible after receiving the school's acceptance letter and ideally two weeks before the school starts.
Because the school demands time and efforts to carry out CPT applications, applying near the deadline could result in CPT I-20 delays. It's possible that this delay could lead to the student unable to start work with CPT on the first-week class.
After receiving the CPT applications, it normally takes the school 3-5 days to process the SEVIS transfer and approve the CPT application. Please start working only after the CPT has been approved. If there is a gap, it is better to take a few days off and keep a record of the day-offs (Do Not including these days on pay stub) in case the USCIS requests RFE to prove that you did not work without authorization.