According to Timatic, the system used by most airlines to confirm visa requirements :
Additional Information: Valid visas in full, invalidated travel
documents are accepted if accompanied by a new travel document.
So yes, your existing visa in your old passport is fine, as long as you present both the old and new passports together.
"Invalidated" here refers to the fact that your existing passport will most likely be physically marked in some way when your new passport is issued (eg, by punching a hole through it, and/or removing the machine readable strip on the biographical page).
Although it doesn't say it here, this generally only applies if none of the biographical information on the passport has changed. ie, the name, date of birth, etc, must match perfectly between both passports. If your name on the new passport is different (eg, due to you getting married between the time the passports were issues) then a new visa would normally be required - although that does vary from country to country.