Carlo Gambino was a very clever man: As you probably know, Vito Genovese arranged with Gambino to assassinate Albert (the Mad Hatter) Anastasia, and to have Gambino take over as Don. In return, Gambino would be loyal to Genovese and support his move to legitimize drug traffic (the purpose of the famous 1957 Apalachin meeting was to legitimize Gambino, anoint Genovese as capo di tutti capi, and to ok drug trafficking). But Neil Dellacroce, who was loyal to Anasasia, vowed to avenge him. So Gambino sat him down and made him an offer he couldn't refuse: Neil would be underboss, and have near-autonomy over the family's "traditional" rackets (loan sharking, hijacking, gambling, etc.). Meanwhile, Gambino was encouraging his cousin and brother in law, Paul Castellano, to develop the family's "white collar" rackets (labor and construction racketeering, legitimate businesses such as wholesale meat and poultry, etc.). Castellano never held a big, official title because Gambino didn't want him to attract law enforcement attention that might have diverted his attempts to develop the "legit" side. But everyone in the family (and the hierarchy of other families) knew that Castellano was at least as high up in Gambino's estimation as Dellacroce.
As it happened, Gambino was on his deathbed while Dellacroce was in jail, finishing a term for tax evasion. The family needed at least an acting boss, and Castellano was it. Castellano's official anointment as head of the family waited a few weeks until Dellacroce got out of prison. He then had a famous sit-down with Dellacroce and promised him the same deal he'd had with Gambino: autonomy over the "blue collar" rackets. Dellacroce accepted.
As you can see, Gambino was lucky as well as clever. The Apalachin meeting was busted up before they were able to name Genovese capo di tutti capi and approve drug trafficking, but they did have time to anoint Gambino. Then Geneovese went away for 15 years on a drug rap, leaving the field clear for Gambino to be the top dog in NYC. And the fact that Gambino had to anoint his own successor while Dellacroce was in prison, worked to his advantage: had Dellacroce been free at the time, he might have fought Castellano for the position no matter what Don Carlo wanted. By the time he got out, Castellano was acting Don and had the blessing of the other families' Dons.