If I don't change the patch after the first week, will it stop working?

You did not write what patch you meant. I suppose about the contraceptive patch Evra. If yes - please read on. Each Evra patch should be removed and replaced immediately with a new one on the same day of the week. If you are delayed by more than two days (48 hours or more) in the middle of the cycle (week two or three) of using the patch, you may not be protected from becoming pregnant. If you do not apply patch number two at all, the first patch will eventually stop releasing hormones in sufficient amounts (some amounts of the active substance can still be released from it), it will not effectively block ovulation, the claimed protection against pregnancy and it is also possible that you will cause earlier withdrawal bleeding. Ultimately, however, the effects are difficult to estimate because the idea you presented is inconsistent with the documentation describing the correct use of Evra. Therefore, I advise against such conduct. In addition, Evra is contraindicated during pregnancy. If you are going to get pregnant, it is wise and safest to simply stop using hormonal contraception. In order not to increase the risk of menstrual disorders and to be able to reliably estimate the beginning of a new cycle, it is recommended to use the current package of hormonal contraception to the end and not to start the next one. I enclose additional information about Evra: https://www.gdziepolek.pl/produkty/28646/evra-system-transdermalny/apteki