You can’t apply for IPO from within Zerodha platform, but you can use the client’s Zerodha DP ID and apply for IPO through his bank account. Almost all banks are giving an online platform to apply for IPO. Since you already have a demat account with Zerodha, you won’t need to open a new one with the bank to apply.
In the bank ASBA IPO form, you need to mention your 16 digit Zerodha DP ID (combination of Depository ID followed by Beneficiary ID you see on the profile page in Q). When the stocks are allotted, it shows up in the Zerodha demat account.