Our custom is to refrain from eating meat during the Nine Days, from Rosh Hodesh Ab until after Tisha B’Ab, except on Shabbat. The question is often asked whether it is permissible to eat after Shabbat meat that is left over from Shabbat. Is this food permissible since it was prepared for Shabbat, or is this food permissible only during Shabbat, but not after Shabbat?
The Halachic authorities permit eating leftover meat from Shabbat on Mosa’eh Shabbat, when it is customary to eat the Melaveh Malka meal. With regard to eating leftovers after Mosa’eh Shabbat, different opinions exist among the Halachic authorities. The Hida (Rav Haim Yosef David Azulai, 1724-1807) writes that there are proofs to both views, and therefore although it is preferable not to eat leftover meat after Mosa’eh Shabbat, those who are lenient in this regard have authorities on whom to rely, and one should not protest against their practice. This is the view followed by Hacham Ovadia Yosef, though he adds that minors (below the age of Bar Misva) may eat leftover meat even Le’chatehila (according to the optimum level of observance). Generally, one should not allow children to eat meat during the Nine Days once they’ve reached the age when they understand the concept of mourning the destruction of the Bet Ha’mikdash. When it comes to Shabbat leftovers, however, since in any event some authorities allow eating such food even beyond Mosa’eh Shabbat, one may feed them to minors.
It should be noted that this applies only to food that was prepared for Shabbat but was not eaten over the course of Shabbat. If one intentionally prepared extra meat before Shabbat in order to have leftovers after Shabbat, it should not be eaten after Shabbat, as this is considered improper "Ha’arama" ("trickery").
Summary: If one has leftover meat from Shabbat during the Nine Days, he may eat it for Melaveh Malka after Shabbat. After Mosa’eh Shabbat, it should not be eaten, but those who are lenient in this regard have authorities on whom to rely. Children below the age of Bar Misva may eat leftover meat even past Mosa’eh Shabbat.