Yes, you can increase time limit for a particular candidate, without affecting the whole test.
If a candidate informs you that they need more time for their test, you can always adjust the time limit for their particular session directly from the Candidate Report.
To access the Candidate Report, you will need to go to either Candidates or Test Mission Control and hover over the candidate in question. A button will appear labeled "Go to report." Select the button, then under Details -> Session Details, you will be able to "Edit time limit" (please note that it can be done only for non-started sessions):
Applying this change doesn't incur any additional costs and it doesn't send any notification to the candidate.
If you have any additional questions about test time limits or would like to leave your feedback, please reach out to your Customer Success Manager or contact us at support@codility.com.