This is a perfectly normal, and typical reaction from your son, so don't worry!
He is exhbiting classic signs of insecurity which are occuring as a result of a seismic change in his little world.
Until now, he has been the only male in your life - the centre of your attention, love and affection.
Suddenly, another male has appaeared, and represents, to his eyes, competition, and the threat of taking over.
It doesn't matter that this is not the case - it's a subconcious response from your son, and needs lots of patient handling.
From you - reassurance that he retains his place in your love and affection, and that your partner is an addition, not a replacement. When you are alone with your son, give him lots of physical affection, and reassure him how important he is, and how much he means to you.
From your partner - reasurance that he loves your son too, and how important your son is to you, and to him - and that he is looking forward to helping your son 'love and look after you', and how he hopes to make both of you happy if he can.
When you are together - lay off the phsyical affection between the two of you, and let your son be affectionate within reason - no clinging or tantrums permitted.
Your son will assimilate the new situation, but it will take a lot of time and patience.
You need to be loving, but firm. Be sure your son's natural selfish instincts (which surface with biological parents as well btw) are not allowed to dominate the family and allow him to manipulate you.
You must must MUST back your partner up in simple discipline issues. Your son will try and play one off against the other - do not allow it to happen, even if you think your partner is wrong, you must back him, and discuss it afterwards when you two are alone - remember it's a learning curve for your partner as well to adapt to loving and looking after a child who