I use an application called time card for Android every time I switch to a new phone I never seem to be able to transfer that app and the data on it which is extremely important to me can anyone help me figure out how to do this as I need to send the old device back as it was a warranty situation
You'll need to do a full backup of that app, i.e. including its data. That usually requires root, but there are some solutions for this specific case to make it work without root – see Full Backup of non-rooted devices. The two candidates you should look at:
adb backup -f <appname>.backup -apk <package_name>
- Helium Backup (an app which does this on-device, but will need to be initialized via ADB)
Note: As Death Mask Salesman correctly pointed out, apps can opt out of ADB backups (developers can include a flag in their apps' Manifests advising the system to not permit ADB to back it up). So if your app falls into that category: bad luck without root.
All your Apps are collected in your account at play store just sign in and you will be able to download it to any device.