Yes, think carefully about it first, and your reasons for deciding to. Definitely find out if there is milage in the relationship before you do, and if in doubt just wait until you know more. Sometimes unfortunately situations dictate how long a relationship lasts even if both people want it to, but to let your child build a friendship with somone new only to have to explain to them that they wont be seeing them again is very confusing for them, and for you.
Absolutely in the early stages after a separation when your child is confused about what is happening and may have feelings of insecurity, then under no circumstances have any situation where anyone comes before them, don’t ever cancel any plans with them or let them down because of someone else.
Sounds like a no-brainer but my last relationship (first serious one after my separation) ended because her children’s father did exactly that, put all his focus into his new partner and frequently let his kids down, things always came up when it was his turn to have them… and in the end she was left having the kids 24/7, with the son refusing to go to see his dad after demonstrating that when he had them over (reluctantly) that they were an inconvenience and in the way. This kind of damage lasts…. don’t be that guy/girl.
Let your kids be involved in any decision about meeting new partners, and let it be their idea. Make absoultely certain they know that any relationship has the potential to be transient whereas they are your focus and nothing will become between you.
I agree with above, make sure this is a happy, healthy relationship that looks like going the distance and introduce the new partner slowly as your ‘best friend’. Try not to spend time all together too soon. There should still be lots of just you and them time, without the new partner around. Luckily for me, my 6 year old has adored my new partner from day one, but she has moments where she feels disloyal to her daddy. I reassure her that daddy is still her daddy and always will be and new partner is her friend, not a new daddy.
I would also tell your ex that you will be introducing a new friend to your child if possible. Otherwise it looks like you are going behind their back. Be calm & firm. They will only be introduced as a friend, and won’t be staying the night initially.
See how your child takes to new partner, and go from there. Good luck.