What's a good idiom or saying to say "don't leave your current job before getting another"?

"A bird in the hand is worth two in the bush,"

It's better to have a lesser but certain advantage than the possibility of a greater one that may come to nothing.

This 16th century proverb is one of the oldest and best-known in English. It warns against taking unnecessary risks - it is better to keep what you have (a bird) than to risk getting more and ending with nothing (two birds out of your reach).

The more classic idiom don't count your chickens (before they're hatched) may apply here. Don't count on your new job and leave the old one till everything is settled:

• something that you say in order to warn someone to wait until a good thing they are expecting has really happened before they make any plans about it.

  • You might be able to get a loan from the bank, but don't count your chickens.

(Cambridge Idioms Dictionary)

Look before you leap.

A common idiomatic caveat, often said to those who may not be considering the downside consequences of a potential change.

This seems to be a good fit, for the cautious and planned versus impulsive mindset you imply in your question.

The metaphor used in my family has always likened this to climbing a ladder...don't release your hold on one rung until you've got a grasp on the next.