One challenge that ballroom dancers find when starting Argentine Tango, is the need to change how the partners in the dance are connected to one another. What needs to change?
Change your frame to an embrace
The tango embrace is much less rigid than the ballroom frame. The hands and arms help the leader and follower communicate as helpers to information from the body, rather than as a rudder system to steer the follower around. It's very subtle, and requires attentive listening from both sides; but is also allows many more variations of movement to happen.
The hands and arms are receptor sites
Think about your hands and arms as receptor sites: you are feeling what the other person is doing, and through your embrace, you can get additional information about the other person's balance, axis and direction.
Instead of steering with the frame, FEEL where your partner is now! Is the follower on axis? Are you both headed the same way in the room? Small, subtle adjustments work much better than "driving" the follower around the room. As a follower, I can feel where the leader is by tuning in with my hands and arms.
Hold your partner like a baby
When you hold a baby, you need to constantly adjust your hold to accommodate the baby's movements. You also need to hold with a firm grip that give the baby reassurance that they are safe. However, if you hold too firmly, the baby feels uncomfortable. All of that applies to holding your partner in tango. If you have never held a baby, think about holding an expensive vase.
A good amount of tone in the arms and hands allows the other person to know that you are present and listening. Just like with a baby, it also calms your partner. I often spend my time dancing with beginners (when leading or following) simply getting them to relax enough to dance, usually by adjusting the energy of my embrace until I feel them relax more.
Relax your elbows!
Let your elbows drop towards the ground ("Energy underside" as one of my students says who does aikido and chi work). Anchor your arms and shoulder blades down into the lower center of your back (latissimus dorsi muscles). The lower they are anchored, the better the other person can read where your body is heading.
Anchor your shoulder blades down, not back
Many ballroom dancers squeeze their shoulder blades together to open up their chest. This is not really a position that will work for hours of dancing! Instead, think about anchoring your shoulder blades DOWN your back. If you have ever seen the wine bottle openers that pull the cork up while the sides of the opener fold down, that's an image I often use to remind folks to slide their shoulder blades down and towards the lower spine.
Let your shoulders and shoulder girdle drape over your torso so that they are balanced, but not tense. Think of a coat, draped over a hanger: the coat is not tense! This will help you dance with a lot less muscle tension and neck/shoulder pain.
Do it all the time!
Again, the more you practice, the faster you learn a new skill. What is you practiced keeping your shoulders relaxed, your elbows released, and your shoulder blades actively anchored down the back ALL THE TIME? Then you would not need to think about that while dancing, and could focus on other parts of the dance!
If you try this out while doing ballroom dance, you will find that most of the tips I have given you will also work in ballroom, and will help relieve tightness in your body while dancing. They will also help you lead and follow better: bonus!