I think there is a mechanism that switches off the transmitter in order to turn on the receiver in the antenna. Do you know the technical terms by which this is done?
A duplexer is an electronic device that allows bi-directional (duplex) communication over a single path. In radar and radio communications systems, it isolates the receiver from the transmitter while permitting them to share a common antenna. Most radio repeater systems include a duplexer. Duplexers can be based on frequency (often a waveguide filter), polarization (such as an orthomode transducer), or timing (as is typical in radar).
The issue isn't necessarily "switching" between reception and transmission, but making sure the receiver doesn't get damaged by the high voltage put onto the antenna by the transmitter. Since the higher level system knows when it's transmitting and when its receiving, it simply ignores the receiver during transmission.
Consider the problem of a receiver. The received RF signals may only be µV, but the transmitter can put 10s or even 100s of volts onto the same node. Note that this problem has been around for a long time, and is not unique to radar. Two-way radios and "walkie talkies" have this problem, as do cell phones.
The solution is generally some kind of switching and/or clamping the signal in the receiver. In a old walkie talkie I had, the push to talk switch physically switched the antenna between the receiver and transmitter, and the speaker between power amp output and microphone amp input. Radar systems need to be much faster, so the switch is electronic. There will also be protection circuitry on the input of the receiver to keep it from getting fried by the inevitable RF that makes it thru the switch even when off. Another issue is recovery time for the receiver. Even if no damage occurs, it may take a little while for the receiver to be able to pick up µV signals again after having been subjected to volts. This all has to be taken into account in the design of the receiver, and the "switch" mechanism may "reach into" the receiver a bit.
At short wavelengths like some radar, it can be possible to use the same pipe bi-directionally. This usually done with waveguides, so is limited to wavelengths short enough to allow the waveguide to be practical in size.
There is no single universal answer to this, but hopefully the above gives you general ideas.