Sorry for the late hit on this.

The apartheid regime, defined as the Nasionale Party's post-1948 governance, was not expansionist in itself. Its attitude towards its neighbors was oddly codependent, and saw the other elements of the High Commission territories (Bechuanaland, Basutoland, and Swaziland, today Botswana, Lesotho, and Eswatini) as the models for the idea of grand apartheid that would fully express under Hendrik Frensch Verwoerd's ministry.

In terms of expansionism, the one case where you may consider it a factor is in South-West Africa (today Namibia), which was given over as a League of Nations Mandate to the Union of South Africa following World War I. Although these mandates were not meant to be taken over, South Africa effectively considered theirs to be a fifth province, and although it was not legally exactly the same it did have reserves, homelands, and seats in the SA parliament after 1950. The UN was very clear that South Africa was holding the territory without agreement to the terms and obligations, so it was an illegal occupation by UN standards (and they first demanded its release in 1976, after castigating South Africa a number of times beforehand). This was not expansion by the apartheid regime, but an attempt at digestion.

Regarding the other HC territories [edit: HC refers to the British High Commission for South Africa, which originally included all Britain's holdings in South Africa from the 1880s onward, as a kind of 'supra-entity' for bureaucratic purposes but that was not politically unified], the British periodically had thoughts of trying to append these to South Africa in order to remove them from Britain's balance sheet. However, the policies of the apartheid regime were anathema to doing so even in 1948, and by that time, the baNgwato royal house had made it clear to the British government that if they attempted to hand Bechuanaland over to Pretoria, the entire Protectorate would go into revolt. As far as all three were concerned, their protectorate agreements with Britain would not permit the British simply to hand over, or sell, or relinquish their protection over those lands even if London really wanted to--and ultimately, the departure of South Africa from the Commonwealth and the fallout of Sharpeville and Rivonia meant that the only way forward was independence. That's why those nations' dates of separation are 1966/1968. Ronald Hyam's old Failure of South African Expansion (1972) is clear about that.

Efforts to acquire Mozambique by purchase or trade, which were floated in Foreign Office files through the First World War, never bore any fruit--again, because this was a charge Britain couldn't justify and South Africa wouldn't shoulder. Portugal was legally an ally, so no seizure was possible.

With all this in mind, however, South Africa absolutely did engage in regional conflict with its neighbors. Although only Malawi--not really a neighbor--ever normalized relations among majority-ruled African nations, the South African response after 1978 to what PW Botha and Magnus Malan called the "Total Onslaught" was definitely region-wide and militant. The SA 'defence forces' were already engaged in periodic incursions against the armed wings of the ANC, PAC (MK and Poqo), and SWAPO (in Namibia, which had begun armed resistance in 1966). Sometimes these actions involved crossing borders or destabilizing newly independent African nations--Angola (already under interference after 1974) and Mozambique (ditto, but initially via Rhodesia) among them, as well as Zimbabwe every so often--but these were not true invasions aside from some of the actions of the Border War with Angola in the 1970s and 1980s. (Gary Baines's book on it is worth a read.) But they had little to no actual diplomatic relationship with those. They had more complicated ties with Lesotho, Swaziland (today Eswatini), and Botswana, but they did not engage in large-scale armed incursions there--these were providers of labor and resources (despite often having laws barring such migrancy), and they could be pressured in other ways to limit their support for ANC/PAC/etc activity. Besides, Britain would view such acts very dimly and Pretoria still needed the tacit support of governments up through Thatcher. BJ Vorster, Prime Minister 1966-1978, did seek to establish diplomatic relations with new African nations but failed in all but one case--Malawi, where money exchanged hands as well.

(I'm not covering relations with the Bantustans/homelands, which were not true neighbors but internal semi-autonomous dependencies regardless of what the Nats ever said.)

So basically, no, there wasn't expansion, but there wasn't really cooperation either; it was a balance of dependency and hostility, except for the temporary example of Malawi.

[edit: explained what the High Commission was.]