I can’t provide direct APK download files, but I can guide you to safely get Google Play Services compatible with Android 7.1.1 and explain installation steps.
You're looking for a way to download Google Play Services for Android 7.1.1. Here are the steps:
Example filename: com.google.android.gms_24.45.33_(100400-12345678)-244533015_minAPI24(armeabi-v7a)(nodpi).apk
If the Play Store is not working, you can download the APK file from a trusted third-party site: Learn about Google Play services - Android Help
Downloading Google Play Services manually comes with risks. Always verify the file signature matches the official Google signature if possible. Avoid downloading ".APK" files from direct download links on forums or ads, as they may contain malware.