Yes, the deposit is deemed to have been repaid to you when the first tenancy ended and immediately paid by you back to the landlord for the second tenancy, so the requirements to protect the deposit applied again at the start of the second tenancy.
That I have been a landlord for over 20 years with no such other claims having been made against me
I have a dedicated bank account to store my deposits in and the DPS automatically protect all deposits within that account
....I will highlight that the following factors will work in my favour to reduce any award made to the lowest possible amount.
Please do let us know how it ends. Too often people come on here for advice and we don't get to know the results.