p- orbitals are directional means that they are oriented in space along particular axis namely , x, y , z axis , the bonding  between metal atoms on account of the force of attraction between free metal ions  and mobile ( frree) electrons is called  metalli bonding. i don't think that they are related to covalent bond in any way

 

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we knw that in case of metals, valence electrons are losely held , it revolves around the core or kernel ( for eg Na⁺ in case of Na) that revolving electron also attracts the adjacent core or kernel by this electron gets sandwiched b/w 2 cores which is nothing bt a mettalic bond.

                                                      

                                               

                                                     

                                                       Na⁺

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                                                       Na⁺