"reserve your place" is correct and usable in written English. You can use it when you want to ask someone to reserve a spot somewhere. For example: If you'd like to attend our event, please reserve your place soon as there are limited spots available.
Call 020 7520 1490 to reserve your place.
The advice is to reserve your place early.
Space is limited, so please reserve your place.
Purchasing tickets at this site with PayPal will reserve your place.
See the CED events calendar for session dates and to reserve your place.
Space is limited so don't forget to reserve your place soon.
"I call it reserving your place in the sun," he said.
Now you can start reserving your place from 14 00 on Tuesday (Swiss time), and once again there's an app for that, which will run on almost any smartphone or tablet you may be carrying and can be downloaded here.
Click here to reserve your free place.
Click here to reserve your delegate place.
Then reserve a place at your key sessions early.
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Claudia Letizia
Head Translator and Proofreader @ organictranslations.eu