It’s not possible to accurately gauge the likelihood of an earlier trademark owner providing consent for your use. It depends primarily on how much the two marks and businesses actually overlap commercially. When the businesses operate in clearly different markets and consumer confusion is genuinely unlikely, earlier owners are more open to consent; there is limited downside for them in allowing a non-competing use.
If the businesses are closely related, obtaining consent is harder. This is because the earlier owner risks diluting their mark's distinctiveness or creating ambiguity about the scope of their rights.
The earlier owner's trademark prosecution history also matters a lot. Some trademark holders are aggressive; others take a more pragmatic view. Starting with a professional, non-confrontational approach; explaining the specific use, the different market position, and the limited scope of the requested consent; gives the conversation the best chance of a positive outcome.