Check out any of these steps and see what best works for you...
1. FIX DATE AND TIME SETTINGS
Google Play Services sync with their master servers to send and receive data,
to do this your device time and date should be correctly set.Follow these steps
>> Go to Settings > Date & Time
>>Check Automatic date & time
>>Or alternatively, you can set time by yourself, just make sure it is correct.
2. CLEAR GOOGLE PLAY STORE APP CACHE
Android OS keeps cache of Google Play Store items in order to quickly serve content
to users and to save bandwidth at same time it might cause some issues and could
be one of the reasons behind connection error.By clearing cache and restarting
the Play Store it will not only resolve the issue but will also
serve you recent/fresh apps for download and purchase
>>Go to Settings > Apps
>>wipe right to ALL
>>Scroll down and tap Google Play Store
>>Press Clear Data button and tap OK
3. CHANGE DNS SETTINGS OF YOUR PHONE OR NETWORK ROUTER
Settings > Select WiFi Network (Hold Tap) > Select Modify > Show Advanced Settings.
* DNS1 should be 8.8.8.8
* DNS2 should be 8.8.4.4
4. CHANGE OR RE-LOGIN YOUR GOOGLE ACCOUNT
>>Go to Settings > Accounts > Google
>>Tap your primary Google account
>>Open options from right top corner, click remove account.
>>Now open Play Store, it will ask you to login your Google account again.
4. CHANGE OR RE-LOGIN YOUR GOOGLE ACCOUNT
If you previously changed the security settings or password of your Google account. You need to update the account settings on your Android device. Also, you can switch to other account.
Remove Google Account in Android
Go to Settings > Accounts > Google
Tap your primary Google account
Open options from right top corner, click remove account.
Now open Play Store, it will ask you to login your Google account again.
5. UNINSTALL UPDATES
>>Go to Google Play App settings (refer to Step #2)
>>Press Uninstall Updates
6. REMOVE ANY PROXY OR VPN SOFTWARE
>>Go to Wireless & Network, modify your WiFi settings, go to advanced options and remove any proxy servers.
>>Disconnect any VPN connection or apps you have running in background.
7. DELETE HOSTS FILE (In case you rooted your device)
>>Open File Manager App.
>>Browse to root/system/etc.
>>Delete hosts.txt file
8. FACTORY RESET YOUR PHONE/TABLET
(Make sure you back-up your contacts and files before you perform a reset, else you will lose everything.)
>>Go to Settings > Backup & reset
>>Click Factory Data Reset