It seems as though you dont have the required permissions to install this PHP extension. This is often the case when youre using shared hosting. The best option is to contact your hosting provider and ask them to install this php extension. However if they provide you with a cpanel dashboard you may be able to do it yourself, heres how:
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Log into your cpanel
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Select your php version, usually under the software section of cpanel
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Select the imagick option and then your options should be saved
And that’s the last step. If you don’t have cPanel your best solution is to contact your hosting provider. If it is a self hosted server you will need to contact the server admin to install the php extension for you. I hope this helps!!