From what I understand, Caesar was assassinated because many senators didn't like how much authority he was receiving, as they were reminded of the earlier kings of Rome and how they always had power over everyone else, which was a big reason as to why Rome transitioned from a monarchy to a republic to begin with. In the case there truly was that much insecurity over one person gaining a high amount of power at the time, then does that mean there were assassination attempts made on the life of Augustus, an emperor?
To answer your question, no. After Caesar's assassination, Augustus was incredibly cautious and ingenious in how he gained and consolidated his power which meant that he was not the victim of any well-known assassination attempts from Republicans.
To begin with, Augustus was never known as 'Emperor'. Instead, he was eventually known as Princeps, 'first citizen', or 'first among men'. His power was slowly consolidated through what we call settlements. The 'first settlement' in 27 BC gave him a new identity as Augustus (previously Octavian) and also gave him permanent consulship in return for him renouncing the powers that he had enjoyed as a Triumvir before the civil war. In 23 BC, the second settlement gave Augustus tribunician power, including the right to speak first in the Senate in return for renouncing permanent consulship - a mere formality, as he was then given extended proconsular authority. In 19 BC, Augustus declared himself as Princeps, and we know of no plots against him after this.
Augustus avoided much of the enmity of staunch Republicans through these slow and ostensible gatherings of power, taking a humble approach and repeatedly claiming that all the power that he had was decreed by the Senate via established traditions. In fact, in his 'Res Gestae', his self-written record of achievements, he claims that he transferred all the power of the Republic to the Senate and People of Rome (Res Gestae 34).
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