If you are still dating or have just started a relationship, it is normal to have some minor insecurities. However, many early indicators can be important to look at, as they (probably) tell a lot about the partner or at least, the potential partner.
Here are some details that may mean he / she has not completely forgotten his / her ex-partner:
1. Still holding photos of the ex.
2. Suggest that you do the same things he / she did with your ex.
3. Mention it in conversations that have nothing to do with it.
4. Make suggestions on how you should act, based on the ways his / her ex acted.
5. Wish her / him a happy birthday.
6. They still have contact with the ex-family, sometimes on a regular basis.
7. They have no problem mentioning them themselves, but if you open it as a topic, they will try to avoid it.
8. Makes excuses when you ask "why don't you post pictures with me".
9. Always react to your ex's posts on social media.
10. If you ask them "why the relationship is not going to another level", try to make excuses.
11. They get emotional when they talk about the ex or hear about him.
12. Most of the stories they tell include him.
13. They often insult your ex, to the point that it becomes annoying.
14. They still have conversations from the ex on the phone.
15. When you ask them why they "still have interactions (of any kind) with their ex", they make excuses.
16. Do not admit to having made any mistake in the previous connection.
17. They talk bad about him, not only to you, but to other people as well.
18. When they receive any news, they call or write to the former in the beginning.
19. They still keep some of his / her belongings at home.
20. You are constantly told that "there is nothing, why are you obsessed, why are you worried in vain, etc.", when you mentioned any of the above points.
Source: Bustle