You can achieve it through the click chemistry reactions (NHS/EDC), Sortase mediated ligation or transglutaminase reaction. But you may have to tweet the protein according to the applied conjugation methods.
Usually this is done by native chemical ligation, reacting a Cys residue on the N-terminus of the protein and a C-terminal thioester on the peptide. The thioester is created by use of a sulfamylbutyryl resin.
If your peptide contains free amines (N-terminal or Lysine's) you would modify with SIA (https://www.thermofisher.com/order/catalog/product/22349) and then, if your protein contains disulfide bonds, reduce some of them with 1-3 eq of TCEP (https://www.thermofisher.com/order/catalog/product/22349) or DTT. Then add the functionalized SIA-Peptide at pH = 8 and the free thiols of the Cys will react with the alfa-carbon binding your peptide to the protein.
On contrary, you should perform the conjugation functionalizing first your protein with SIA and then if your peptide contains thiol groups, perform the conjugation reaction.
Another option is to modify the protein with the Maleimidogroup (i.e. MBS). Excess of reagent is removed by a PD10 column. Modify your peptide with an N-terminal Cystein. Coupling of the protein and the Cys-peptide is achieved in minutes at pH 7.2 under smooth condition in PBS. I use this method since years for the synthesis of immunogens. You may ask for exact conditions.