“Immediately.” That means right away; no waiting. In general, the most appropriate time to use this term is when defining when a right becomes exercisable. For example, Article 628 of the Civil Code:
当事者が雇用の期間を定めた場合であっても、やむを得ない事由があるときは、各当事者は、直ちに契約の解除をすることができる。Even in cases where the parties have specified the term of employment, if there are unavoidable reasons, either party may immediately cancel the contract.
Unfortunately, this term is often used, incorrectly, to describe when things need to be done, as in Article 337 of the Civil Code:
不動産の保存の先取特権の効力を保存するためには、保存行為が完了した後直ちに登記をしなければならない。In order to preserve the effectiveness of statutory liens for preservation of immovable properties, registration must be carried out immediately after the completion of the act of preservation.
Read very literally, this would seem to mean that the lien holder needs to be at the registration office at the moment they commit an act of preservation. (Of course, this is not how the Japanese government bureaucrats or courts would interpret the statute in practice; they are more reasonable than the authors of the law.)
The softest alternative to this word is 遅滞なく (entai naku), meaning “without delay.” In practice, this phrase is interpreted more like the English phrase “without unreasonable delay,” meaning that delay is allowed only on reasonable grounds.
In between the two is the phrase 速やかに (sumiyaka ni), meaning “promptly.” The meaning of this term is murkier and open to interpretation depending upon the circumstances. In fact, the vagueness of the term was used to challenge the validity of a criminal statute that included it, but an Osaka High Court decision in 1972 found that the term was clear enough to be interpreted by a court, even though opinions could differ as to what is and is not “prompt.”