Does tearing clothing imply nakedness?
No, not necessarily.
Does it mean that Tamar was going naked around Jerusalem?
No. She did not tear her undergarment.
2 Samuel 13:19 Tamar put ashes on her head and tore the ornate robe she was wearing.
Similarly for the priests:
Exodus 28:42 “Make linen undergarments as a covering for the body, reaching from the waist to the thigh. 43Aaron and his sons must wear them whenever they enter the tent of meeting or approach the altar to minister in the Holy Place, so that they will not incur guilt and die.
“This is to be a lasting ordinance for Aaron and his descendants.
Mark 14:63 The high priest tore his clothes. "Why do we need any more witnesses?" he asked.
It was a symbolic act. It was not necessary that the high priest tore his undergarment and it is forbidden if he was in the Holy Place.
The symbolic point was not necessarily to expose the flesh. If it were, why bothered covering yourself with sackcloth afterward.
2 Kings 19:1 When King Hezekiah heard this, he tore his clothes and put on sackcloth and went into the temple of the LORD.
Esther 4:1 When Mordecai learned of all that had been done, he tore his clothes, put on sackcloth and ashes, and went out into the city, wailing loudly and bitterly.
Joshua 7:6Then Joshua tore his clothes and fell facedown to the ground before the ark of the LORD, remaining there till evening. The elders of Israel did the same, and sprinkled dust on their heads.
1 Kings 21:27 When Ahab heard these words, he tore his clothes, put on sackcloth and fasted. He lay in sackcloth and went around meekly.
Genesis 37:34 Then Jacob tore his clothes, put on sackcloth and mourned for his son many days.
Having said all the above, if a person didn't have any undergarment on, then tearing clothes would expose the flesh. Also, there was nothing to prevent some to tore their immediate undergarment either.
2 Samuel 1:11-12 Then David and all the men with him took hold of their clothes and tore them. They mourned and wept and fasted till evening for Saul and his son Jonathan, and for the army of the Lord and for the nation of Israel, because they had fallen by the sword.
Some of these David's macho guys might have exposed their chests.
In conclusion, I do not see the symbolic act require exposing flesh but it didn't prevent it either.