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No, updating apps, which is what it sounds like you have been prompted to do, will not free any storage space....or at least, very little. The way to do that is to delete some unneeded apps, or some of your personal data such as photos, music, downloads, etc., or to move them to external storage, such as cloud storage or SD card, if your device will take an SD card.
Go to Settings, Storage, and you will see the different categories of stored data. Some cannot be deleted, but you can certainly delete the Cached Data.
Get back to us if you need any advice on how best to proceed. Mention which model of HTC Desire you have.
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